Atomic weights of the elements 2007
3.
2153
ported isotope-amount ratios are evaluated and, if needed, uncertainties are expanded to cover possible systematic errors in the measurements. Reported values are corrected only if there is sufficient information in the publication for reliable estimation of systematic offsets. Details on the mathematical approach for expanding uncertainties of published isotope ratios are given below. After calculation using GUM Workbench software, isotope-amount ratios, molar fractions, and the atomic weight with their (expanded) standard uncertainties are exported back to the element database.
For evaluating uncertainties of published isotope-amount ratios, the following sources of systematic errors, at a minimum, should be considered where x represents possible systematic offsets and k represents the corresponding correction factor: 1. 2. 3. 4. 5.
System linearity Baseline correction Isobaric interferences Instrumental fractionation Sample preparation
xl xb xi xf xp
kl kb ki kf kp
For the correction of systematic offsets, a correction factor is introduced that carries an uncertainty k = x ± u(x) where k is the correction factor for a potential systematic error and u(x) is the uncertainty of the correction factor. Both k and u(x) may be different for individual isotope ratios of an element. Unless it is possible to calculate or estimate a reliable systematic offset from published isotope ratios, x will be set to 1. When considering the above sources of uncertainty, the corrected isotope-number ratio R can be expressed as R = r ⴢ kl ⴢ kb ⴢ ki ⴢ kf ⴢ kp where r is the published isotope-amount ratio. Applying the laws of error propagation, the relative uncertainty of R, (u(R)/R), is given by
( )
( )
( )
( ) ⎞⎟
2 2 2 ⎛ 2 u kf ⎛ u kl ⎞ ⎛ u kb ⎞ ⎛ u ki ⎞ ⎛u r ⎞ u ( R) = ⎜ ⎟ +⎜ ⎟ +⎜ ⎟ +⎜ ⎟ +⎜ R ⎜ kf ⎝ r ⎠ ⎝ kl ⎠ ⎝ kb ⎠ ⎝ ki ⎠ ⎝
()
2
( ) ⎞⎟
⎛u k p +⎜ ⎟ ⎜ kp ⎠ ⎝
2
⎟ ⎠
Because no reported isotope-ratio value will be revised unless the magnitude of a systematic offset in the data can be assessed from published information, k always equals 1. The Commission considers the following systematic offsets when reviewing publications. As far as possible, the measurement modes or measurement conditions are listed in descending order in relation to the possible magnitude of the offset. 1.
2.
Offsets due to system nonlinearity (kl) • fully calibrated measurement (including a linearity check) • Faraday cup(s) for ion detection single collector multicollector (use of a virtual amplifier system; correction for differences in cup efficiency; use of gain factors for each individual cup) • secondary electron multiplier(s) for ion detection (single ion counting, continuous mode) Offsets due to baseline effects (kb) • detector system (Faraday cup(s) or secondary electron multipliers) • measurement mode (on peak/between peaks, closed valve/open valve, between scans/blocks/measurements)
© 2009 IUPAC, Pure and Applied Chemistry 81, 2131–2156